Abstract: A6.00005 : Negative-weight percolation*

Author:

Alexander Hartmann(University of Oldenburg, Germany)

We describe a percolation problem on lattices (graphs, networks),
with edge weights
drawn from disorder distributions that allow for weights (or
distances)
of either sign, i.e. including negative weights. We are
interested whether
there are spanning paths or loops of total negative weight.
This kind of percolation problem
is fundamentally different from conventional percolation problems,
e.g. it does not exhibit transitivity, hence no simple definition
of clusters, and several spanning paths/loops might coexist in
the percolation
regime at the same time. Furthermore, to study this percolation
problem
numerically, one has to perform a non-trivial transformation of the
original graph and apply sophisticated matching algorithms.
Using this approach, we study the corresponding percolation
transitions on large square, hexagonal and cubic
lattices for two types of disorder
distributions and determine the
critical exponents. The results show that negative-weight
percolation
is in a different universality class compared to conventional
bond/site percolation. On the other hand, negative-weight percolation
seems to be related to the
ferromagnet/spin-glass transition of random-bond Ising systems, at
least in two dimensions.
Furthermore, results for diluted lattices and higher dimensions
up to d=7 are presented, to address, respectively,
questions of (non-)universality
and the transition to mean-field behavior at the upper critical
dimension.

*supported from Volkswagen Foundation

To cite this abstract, use the following reference: http://meetings.aps.org/link/BAPS.2010.MAR.A6.5